The world is a dangerous place. Earthquakes, floods, wildfires, volcanoes, droughts, hurricanes and tornadoes reshape the land, destroy lives and lay waste to entire communities. Some of these perils — hurricanes, for example — often hit with enough warning that people can prepare and, if need be, get out of way. Others, however, frequently arrive with no warning, at all, or with so little warning that the only thing anyone can do is try to find a safe place to ride it out. A doorway during an earthquake, for example. Or a basement when, out of a troubled sky, a tornado suddenly touches down, roaring (as so many survivors characterize the sound) like a freight train from hell.

Here, in the very midst of tornado season, LIFE.com recalls a catastrophic tornado that slammed into Waco, Texas, 60 years ago this week. On the afternoon of May 11, 1953, an F5 tornado made a direct hit on Waco. (On the scale for rating rotational intensity created by storm researcher Ted Fujita, an F5 twister is capable of “incredible damage.) In a matter of minutes, in the face of cyclonic winds that likely topped 300 mph, hundreds of homes and businesses were utterly destroyed; thousands of cars were damaged or totaled; almost 600 people were injured and 114 were killed.

Today, six decades later, the 1953 Waco tornado remains tied with the 1902 Goliad twister for the grim distinction of Texas’s deadliest, and is the 11th deadliest in U.S. history.

In the immediate aftermath of the tornado, LIFE’s John Dominis and correspondent Scot Leavitt, who had just recently moved to Texas, made their way to the devastated city. All of the photos in this gallery, many of which never ran in LIFE, are Dominis’s; in a note sent to LIFE’s editors in New York, Leavitt noted that “through virtually all [of Dominis’s] shooting, rain fell, the sky was dark and the mood was somber.”

For its part, LIFE wrote of the disaster in its May 25, 1953 issue:

By May 11 the warm, close weather was uncomfortably routine to the people of Waco, Texas. The day before had been muggy and the day before that, too. The big news in the Morning News-Tribune was of a tornado in far-off Minnesota. At mid-morning the New Orleans weather bureau warned there might be a few tornadoes close to home. But an Indian belief that tornadoes would never strike Waco had always held true and no one in the city worried about the report At 1:30 .m. the Waco weather forecaster announced, “No cause for alarm.”

Three hours later the skies suddenly darkened. people scurried for shelter from the hail and slashing rain, and at the edge of town a cemetery workman looked up to see a thick black wedge forming under a low cloud … At 4:37 p.m. the black wedge in the sky struck Fifth and Austin [streets], gouged the earth for a block and left the heart of Waco a broken coffin for scores of schoolboys, housewives, motorists….